Next Greater Numerically Balanced Number — C++

// Time:  O(logc) = O(1)
// Space: O(c) = O(1)

class Solution {
public:
    int nextBeautifulNumber(int n) {
        // precomputed by generating all balanced's permutations in solution2
        static const vector<int> candidates =  {
                 1,     22,    122,    212,    221,    333  , 1333,   3133,   3313,   3331,
              4444,  14444,  22333,  23233,  23323,  23332,  32233,  32323,  32332,  33223,
             33232,  33322,  41444,  44144,  44414,  44441,  55555, 122333, 123233, 123323,
            123332, 132233, 132323, 132332, 133223, 133232, 133322, 155555, 212333, 213233,
            213323, 213332, 221333, 223133, 223313, 223331, 224444, 231233, 231323, 231332,
            232133, 232313, 232331, 233123, 233132, 233213, 233231, 233312, 233321, 242444,
            244244, 244424, 244442, 312233, 312323, 312332, 313223, 313232, 313322, 321233,
            321323, 321332, 322133, 322313, 322331, 323123, 323132, 323213, 323231, 323312,
            323321, 331223, 331232, 331322, 332123, 332132, 332213, 332231, 332312, 332321,
            333122, 333212, 333221, 422444, 424244, 424424, 424442, 442244, 442424, 442442,
            444224, 444242, 444422, 515555, 551555, 555155, 555515, 555551, 666666, 1224444
        };
        return *upper_bound(cbegin(candidates), cend(candidates), n);
    }   
};

// Time:  O(l * c) = O(1), c is the count of all balanced's permutations, l is the max length of permutations
// Space: O(l * b) = O(1), b is the count of balanced
class Solution2 {
public:
    int nextBeautifulNumber(int n) {
        // obtained by manually enumerating min number of permutations in each length
        static const vector<int> balanced = {
            1,
            22,
            122, 333,
            1333, 4444,
            14444, 22333, 55555,
            122333, 155555, 224444, 666666
        };
        const auto& s = to_string(n);
        int result = 1224444;
        for (const auto& i : balanced) {
            auto x = to_string(i);
            if (size(x) < size(s)) {
                continue;
            }
            if (size(x) > size(s)) {
                result = min(result, stoi(x));
                continue;
            }
            while (true) {
                if (x > s) {
                    result = min(result, stoi(x));
                }
                if (!next_permutation(begin(x), end(x))) {
                    break;
                }
            }
        }
        return result;
    }   
};